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I have estimated a log linear regression model using SAS with the following functional form:
lnY = a + XB1 + Xb2 + Xb3 + Xb4
The dependent variable is in log form, the independent/explanatory variables in linear form.
With the equation I can estimate/forecast the linear value of Y by taking the antilog/exponent of the forecast from the equation so that I can see the value in the orginal Y values instead of the logs. This is fine.
But I also want to decompose the forecast/estimate by the respective explanatory X variable.
For example if the total forecast in log form = 5, then the anti log/exponent of that gives me a forecast of 148 in the original Y series. Now of that 148, what I need to calculate is how much is X1, X2 etc is worth, e.g
a = 2
X1 = 45
X2 = 15
X3 = 25
x4 = 61
Total = 148
Does anyone know how to do this?
Hey Bishu!! Long time.. I was pretty much looking for something similar since I ended up doing log-linear for a market mix project.
As far as I can tell, there's no easy way to land at decompositions for a log-linear model. Log transformed models lose all relations to the original variable, and the multiplicity of the explanatory vars end up making it difficult to say what % of something caused something. Elasticities are available ofcourse.
There's 2 approx. methods though that I came across that might help - 'Purging Method' and 'Delta Method' that help approximate the % contribution.
(And I can tell the other person who commented has no idea what you're asking! Lol.)
Arun (let's see if you recognize who this is!)